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Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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08 Jan 2016, 23:48

8

3

shasadou wrote:

If xy < zy < 0, is y positive?

(1) x < z (2) x is negative

xy < zy < 0 Both xy and zy are negative. Either y is negative, x and z both are positive and x > z. Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)
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Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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20 Feb 2019, 09:47

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Top Contributor

shasadou wrote:

If xy < zy < 0, is y positive?

(1) x < z (2) x is negative

Target question:Is y positive?

Given: xy < zy < 0, Let's focus on this part of the inequality: xy < zy Subtract xy from both sides to get: 0 < zy - xy Factor out the y to get: 0 < y(z - x) (this will come in handy later)

Statement 1: x < z Subtract x from both sides to get: 0 < z - x In other words, (z - x) is POSITIVE This means we can take our given inequality 0 < y(z - x) and divide both sides by (z - x) to get: 0 < y So, the answer to the target question is YES, y IS positive Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is negative The given information tells us that xy < zy < 0 This means xy < 0 In other words, xy is NEGATIVE So, if x is negative, then it MUST be the case that y is POSITIVE Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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10 Jan 2016, 19:13

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If xy < zy < 0, is y positive?

(1) x < z (2) x is negative

When you modify the original condition and the question, it becomes (x-z)y<0에서 y>0? --> x-z<0?. x<Z에서 1) is yes, which is sufficient. For 2), if x<0, y>0 derived from xy<0, which is yes and sufficient. Therefore, the answer is D.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________

If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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23 Jul 2018, 11:44

KarishmaB wrote:

shasadou wrote:

If xy < zy < 0, is y positive?

(1) x < z (2) x is negative

xy < zy < 0 Both xy and zy are negative. Either y is negative, x and z both are positive and x > z. Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0; I agree for option 1 is sufficient on the basis that x<z; for the second option, since x is -ve x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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23 Jul 2018, 11:54

harish1986 wrote:

KarishmaB wrote:

shasadou wrote:

If xy < zy < 0, is y positive?

(1) x < z (2) x is negative

xy < zy < 0 Both xy and zy are negative. Either y is negative, x and z both are positive and x > z. Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0; I agree for option 1 is sufficient on the basis that x<z; for the second option, since x is -ve x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??

From Statement 2, we don't get any information for z & we are not bothered about z, all we need to figure out is whether y > 0

We know from question prompt that xy < 0, hence if x < 0, then y > 0

Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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23 Jul 2018, 11:56

harish1986 wrote:

KarishmaB wrote:

shasadou wrote:

If xy < zy < 0, is y positive?

(1) x < z (2) x is negative

xy < zy < 0 Both xy and zy are negative. Either y is negative, x and z both are positive and x > z. Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0; I agree for option 1 is sufficient on the basis that x<z; for the second option, since x is -ve x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??

The #'s plugged in are not correct x < z, hence x=-5 and z=-10 is not valid
_________________

Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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18 Nov 2019, 05:17

Official explanation

Solution: D

This difficult inequality problem requires that you properly leverage the information from the question stem. The second statement is relatively easy so you should start there – if x is negative and xy is negative then y must be positive. The second statement is sufficient. Since the second statement is relatively straightforward you should expect the 1st statement to be harder: from the question stem you know that xy < zy. If y were positive then you could divide by y and see that x < z. If y were negative then you could divide both sides to see that x > z. Since statement 1 proves that x < z then it must be the first case and y must be positive. Answer is D. Number picking is awkward and time consuming on first statement so don’t forget to use algebra as your first approach in any inequality problem.

Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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01 Dec 2019, 12:55

xy<zy<0.

Tip 1: xy<zy, cancel y.. x<z.. dont do that. This is because you dont know what y is (positive or negative)

So, xy<zy, or, xy-zy<0, or, y(x-z)<0.

So, Either y<0, therefore in this case, (x-z)>0 .....(i) OR, (x-z)<0, therefore in this case, y>0 ........(ii)

(1) x<z, which means (x-z)<0, which means equation (ii) is valid. y>0. SUFFICIENT (2) x is negative, we know xy<0, if x negative, then y must be positive. SUFFICIENT

Answer: D

gmatclubot

Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative
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01 Dec 2019, 12:55